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Weiye Yao and Christiane Jablonowski

Abstract

The paper demonstrates that quasi-biennial oscillation (QBO)-like oscillations can be simulated in an ensemble of dry GCM dynamical cores that are driven by a simple Held–Suarez temperature relaxation and low-level Rayleigh friction. The tropical stratospheric circulations of four dynamical cores, which are options in NCAR’s Community Atmosphere Model, version 5 (CAM5), are intercompared. These are the semi-Lagrangian (SLD) and Eulerian (EUL) spectral transform, finite-volume (FV), and spectral element (SE) dynamical cores. The paper investigates how the model design choices impact the wave generation, propagation, and dissipation mechanisms in the equatorial region. SLD, EUL, and SE develop spontaneous QBO-like oscillations in the upper equatorial stratosphere, whereas FV does not sustain the oscillation. Transformed Eulerian-mean (TEM) analyses reveal that resolved waves are the dominant drivers of the QBOs. However, the Eliassen–Palm flux divergence is strongly counteracted by the TEM momentum budget residual, which represents the forcing by diffusion and thermal damping. Interestingly, a reversed Brewer–Dobson circulation accelerates the downward propagation of the SLD’s QBO, whereas the EUL’s and SE’s QBOs are slowed by a mean ascent. Waves are abundant in the SLD’s, EUL’s, and SE’s tropical atmosphere despite the absence of moist convection as a typical wave trigger. Dynamic instabilities are suggested as a wave-triggering mechanism in the troposphere and wave-dissipation process in the stratosphere. In particular, there are indications that the increased occurrences of strongly negative instability indicators in SLD, EUL, and SE are related to more vigorous wave activities and higher magnitudes of the resolved wave forcing in comparison to FV.

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Weiye Yao and Christiane Jablonowski

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The paper demonstrates that sudden stratospheric warmings (SSWs) can be simulated in an ensemble of dry dynamical cores that miss the typical SSW forcing mechanisms like moist processes, land–sea contrasts, or topography. These idealized general circulation model (GCM) simulations are driven by a simple Held–Suarez–Williamson (HSW) temperature relaxation and low-level Rayleigh friction. In particular, the four dynamical cores of NCAR’s Community Atmosphere Model, version 5 (CAM5), are used, which are the semi-Lagrangian (SLD) and Eulerian (EUL) spectral-transform models and the finite-volume (FV) and the spectral element (SE) models.

Three research themes are discussed. First, it is shown that SSW events in such idealized simulations have very realistic flow characteristics that are analyzed via the SLD model. A single vortex-split event is highlighted that is driven by wavenumber-1 and -2 wave–mean flow interactions. Second, the SLD simulations are compared to the EUL, FV, and SE dynamical cores, which sheds light on the impact of the numerical schemes on the circulation. Only SLD produces major SSWs, while others only exhibit minor stratospheric warmings. These differences are caused by SLD’s more vigorous wave–mean flow interactions in addition to a warm pole bias, which leads to relatively weak polar jets in SLD. Third, it is shown that tropical quasi-biennial oscillation (QBO)–like oscillations and SSWs can coexist in such idealized HSW simulations. They are present in the SLD dynamical core that is used to analyze the QBO–SSW interactions via a transformed Eulerian-mean (TEM) analysis. The TEM results provide support for the Holton–Tan effect.

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Paul Ullrich and Christiane Jablonowski

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This paper presents a new approach for discretizing the nonhydrostatic Euler equations in Cartesian geometry using an operator-split time-stepping strategy and unstaggered upwind finite-volume model formulation. Following the method of lines, a spatial discretization of the governing equations leads to a set of coupled nonlinear ordinary differential equations. In general, explicit time-stepping methods cannot be applied directly to these equations because the large aspect ratio between the horizontal and vertical grid spacing leads to a stringent restriction on the time step to maintain numerical stability. Instead, an A-stable linearly implicit Rosenbrock method for evolving the vertical components of the equations coupled to a traditional explicit Runge–Kutta formula in the horizontal is proposed. Up to third-order temporal accuracy is achieved by carefully interleaving the explicit and linearly implicit steps. The time step for the resulting Runge–Kutta–Rosenbrock–type semi-implicit method is then restricted only by the grid spacing and wave speed in the horizontal. The high-order finite-volume model is tested against a series of atmospheric flow problems to verify accuracy and consistency. The results of these tests reveal that this method is accurate, stable, and applicable to a wide range of atmospheric flows and scales.

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Kevin A. Reed and Christiane Jablonowski

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The paper discusses the design of idealized tropical cyclone experiments in atmospheric general circulation models (AGCMs). The evolution of an initially weak, warm-core vortex is investigated over a 10-day period with varying initial conditions that include variations of the maximum wind speed and radius of maximum wind. The initialization of the vortex is built upon prescribed 3D moisture, pressure, temperature, and velocity fields that are embedded into tropical environmental conditions. The initial fields are in exact hydrostatic and gradient-wind balance in an axisymmetric form. The formulation is then generalized to provide analytic initial conditions for an approximately balanced vortex in AGCMs with height-based vertical coordinates. An extension for global models with pressure-based vertical coordinates is presented. The analytic initialization technique can easily be implemented on any AGCM computational grid.

The characteristics of the idealized tropical cyclone experiments are illustrated in high-resolution model simulations with the Community Atmosphere Model version 3.1 (CAM 3.1) developed at the National Center for Atmospheric Research. The finite-volume dynamical core in CAM 3.1 with 26 vertical levels is used, and utilizes an aquaplanet configuration with constant sea surface temperatures of 29°C. The impact of varying initial conditions and horizontal resolutions on the evolution of the tropical cyclone–like vortex is investigated. Identical physical parameterizations with a constant parameter set are used at all horizontal resolutions. The sensitivity studies reveal that the initial wind speed and radius of maximum wind need to lie above a threshold to support the intensification of the analytic initial vortex at horizontal grid spacings of 0.5° and 0.25° (or 55 and 28 km in the equatorial regions). The thresholds lie between 15 and 20 m s−1 with a radius of maximum wind of about 200–250 km. In addition, a convergence study with the grid spacings 1.0°, 0.5°, 0.25°, and 0.125° (or 111, 55, 28, and 14 km) shows that the cyclone gets more intense and compact with increasing horizontal resolution. The 0.5°, 0.25°, and 0.125° simulations exhibit many tropical cyclone–like characteristics such as a warm-core, low-level wind maxima, a slanted eyewall-like vertical structure and a relatively calm eye. The 0.125° simulation even starts to resolve spiral rainbands and reaches maximum wind speeds of about 72–83 m s−1 at low levels. These wind speeds are equivalent to a category-5 tropical cyclone on the Saffir–Simpson hurricane scale. It is suggested that the vortex initialization technique can be used as an idealized tool to study the impact of varying resolutions, physical parameterizations, and numerical schemes on the simulation and representation of tropical cyclone–like vortices in global atmospheric models.

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Colin M. Zarzycki and Christiane Jablonowski

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Tropical cyclone (TC) forecasts at 14-km horizontal resolution (0.125°) are completed using variable-resolution (V-R) grids within the Community Atmosphere Model (CAM). Forecasts are integrated twice daily from 1 August to 31 October for both 2012 and 2013, with a high-resolution nest centered over the North Atlantic and eastern Pacific Ocean basins. Using the CAM version 5 (CAM5) physical parameterization package, regional refinement is shown to significantly increase TC track forecast skill relative to unrefined grids (55 km, 0.5°). For typical TC forecast integration periods (approximately 1 week), V-R forecasts are able to nearly identically reproduce the flow field of a globally uniform high-resolution forecast. Simulated intensity is generally too strong for forecasts beyond 72 h. This intensity bias is robust regardless of whether the forecast is forced with observed or climatological sea surface temperatures and is not significantly mitigated in a suite of sensitivity simulations aimed at investigating the impact of model time step and CAM’s deep convection parameterization. Replacing components of the default physics with Cloud Layers Unified by Binormals (CLUBB) produces a statistically significant improvement in forecast intensity at longer lead times, although significant structural differences in forecasted TCs exist. CAM forecasts the recurvature of Hurricane Sandy into the northeastern United States 60 h earlier than the Global Forecast System (GFS) model using identical initial conditions, demonstrating the sensitivity of TC forecasts to model configuration. Computational costs associated with V-R simulations are dramatically decreased relative to globally uniform high-resolution simulations, demonstrating that variable-resolution techniques are a promising tool for future numerical weather prediction applications.

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Ramachandran D. Nair and Christiane Jablonowski

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A new two-dimensional advection test on the surface of the sphere is proposed. The test combines a solid-body rotation and a deformational flow field to form moving vortices over the surface of the sphere. The resulting time-dependent deforming vortex centers are located on diametrically opposite sides of the sphere and move along a predetermined great circle trajectory. The horizontal wind field is deformational and nondivergent, and the analytic solution is known at any time. During one revolution around the sphere the initially smooth transported scalar develops strong gradients. Such an approach is therefore more challenging than existing advection test cases on the sphere. To demonstrate the effectiveness and versatility of the proposed test, three different advection schemes are employed, such as a discontinuous Galerkin method on a cubed-sphere mesh, a classical semi-Lagrangian method, and a finite-volume algorithm with adaptive mesh refinement (AMR) on a regular latitude–longitude grid. The numerical results are compared with the analytic solution for different flow orientation angles on the sphere.

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Jared O. Ferguson, Christiane Jablonowski, and Hans Johansen

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Two forced shallow-water flow scenarios are explored in a 2D fourth-order finite-volume dynamical core with adaptive mesh refinement (AMR) to investigate AMR’s ability to track and resolve complex evolving features. Traditional shallow-water test cases are mainly characterized by large-scale smooth flows that do not effectively test the multiscale abilities of variable-resolution and AMR models to resolve sharp gradients and small-scale flow filaments. Therefore, adding forcing mechanisms to the shallow-water system to model key atmospheric processes adds complexity and creates small-scale phenomena. These can serve as foci for dynamic grid refinement while remaining simple enough to study the numerical design of a model’s dynamical core. The first shallow-water flow scenario represents a strengthening, tropical cyclone–like, vortex that is driven by a Betts–Miller-like convection scheme. The second shallow-water test is built upon a barotropically unstable jet with an added Kessler-like warm rain scheme that leads to precipitating frontal zones. The key feature of both tests is that there is significant sensitivity to the model grid while converging (structurally) at high resolution. Both test cases are investigated for a series of uniform resolutions and a variety of AMR tagging criteria. The AMR simulations demonstrate that grid refinement can resolve local features without requiring global high-resolution meshes. However, the results are sensitive to the refinement criteria. Criteria that trigger refinement early in a simulation reproduce the uniform-resolution reference solutions most reliably. In contrast, AMR criteria that delay refinement for several days require careful tuning of the AMR thresholds to improve results compared with uniform-resolution simulations.

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Paul A. Ullrich, Peter H. Lauritzen, and Christiane Jablonowski

Abstract

Land, ocean, and atmospheric models are often implemented on different spherical grids. As a conseqence coupling these model components requires state variables and fluxes to be regridded. For some variables, such as fluxes, it is paramount that the regridding algorithm is conservative (so that energy and water budget balances are maintained) and monotone (to prevent unphysical values). For global applications the cubed-sphere grids are gaining popularity in the atmospheric community whereas, for example, the land modeling groups are mostly using the regular latitude–longitude grid. Most existing regridding schemes fail to take advantage of geometrical symmetries between these grids and hence accuracy of the calculations can be lost. Hence, a new Geometrically Exact Conservative Remapping (GECoRe) scheme with a monotone option is proposed for remapping between regular latitude–longitude and gnomonic cubed-sphere grids. GECoRe is compared with existing remapping schemes published in the meteorological literature. It is concluded here that the geometrically exact scheme significantly improves the accuracy of the resulting remapping in idealized test cases.

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David L. Williamson, Jerry G. Olson, and Christiane Jablonowski

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Two flaws in the semi-Lagrangian algorithm originally implemented as an optional dynamical core in the NCAR Community Atmosphere Model (CAM3.1) are exposed by steady-state and baroclinic instability test cases. Remedies are demonstrated and have been incorporated in the dynamical core. One consequence of the first flaw is an erroneous damping of the speed of a zonally uniform zonal wind undergoing advection by a zonally uniform zonal flow field. It results from projecting the transported vector wind expressed in unit vectors at the arrival point to the surface of the sphere and is eliminated by rotating the vector to be parallel to the surface. The second flaw is the formulation of an a posteriori energy fixer that, although small, systematically affects the temperature field and leads to an incorrect evolution of the growing baroclinic wave. That fixer restores the total energy at each time step by changing the provisional forecast temperature proportionally to the magnitude of the temperature change at that time step. Two other fixers are introduced that do not exhibit the flaw. One changes the provisional temperature everywhere by an additive constant, and the other changes it proportionally by a multiplicative constant.

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Colin M. Zarzycki, Christiane Jablonowski, and Mark A. Taylor

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A statically nested, variable-mesh option has recently been introduced into the Community Atmosphere Model’s (CAM's) Spectral Element (SE) dynamical core that has become the default in CAM version 5.3. This paper presents a series of tests of increasing complexity that highlight the use of variable-resolution grids in CAM-SE to improve tropical cyclone representation by dynamically resolving storms without requiring the computational demand of a global high-resolution grid. As a simplified initial test, a dry vortex is advected through grid transition regions in variable-resolution meshes on an irrotational planet with the CAM subgrid parameterization package turned off. Vortex structure and intensity is only affected by grid resolution and no spurious artifacts are observed. CAM-SE model simulations using an idealized tropical cyclone test case on an aquaplanet show no numerical distortion or wave reflection when the cyclone interacts with an abrupt transition region. Using the same test case, the authors demonstrate that a regionally refined mesh with significantly fewer degrees of freedom can produce the same local results as a globally uniform grid. Additionally, the authors discuss a more complex aquaplanet experiment with meridionally varying sea surface temperatures that reproduces a quasi-realistic global climate. Tropical cyclogenesis is facilitated without the need for vortex bogusing in a high-resolution patch embedded within a global grid that is otherwise too coarse to resolve realistic tropical cyclones in CAM.

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